two_heads_talking wrote:What's that got to do with voting? I've made up my mind by the time I hit the booth. I'm not swayed by the knuckle draggers who stand outside holding up signs of their favorite candidate. I usually tell them to quit wasting their breath on me..

You know. Seeing both sides, yada yada yada. Staring at the ballot. Well, the R guy is good, but the D guy is good too...

Infidel wrote:I actually meant bi-polar for simplicity and wrote two-dimensional for some reason. Not that I'm accusing two dimensional thinkers of ordering complex numbers. Not at all. I'm accusing them of artificially reducing complex numbers to real numbers, more often to just natural numbers, so it fits within their narrow sphere of thought. E.g. they take a chair and reduce it to four points on a plane then connect the dots and claim a chair is a square. That is if they don't claim that the four points are obviously unrelated.

Uh wait ... thinkers? Were we not talking about Maths and Hyperuranium?
Anyway I agree. A good novel about this and this metaphor is Flatland.

Infidel wrote:Even if complex numbers cannot be ordered in two dimensions, real numbers can be.

Real numbers can be ordered, but I think I don't understand how they can in two dimensions (or any dimensions greater than 1)...

astaroth wrote:
Real numbers can be ordered, but I think I don't understand how they can in two dimensions (or any dimensions greater than 1)...

I don't believe in a single dimension since dimensions are really just mathematical constructs to simplify equations, not a different place, rather it's the same place presented with a different perspective. Thus, if the math fails then the problem has been oversimplified and values for the missing dimensions should be plugged in. A line is just a plane with a width of zero.

Infidel wrote:
I don't believe in a single dimension since dimensions are really just mathematical constructs to simplify equations, not a different place, rather it's the same place presented with a different perspective. Thus, if the math fails then the problem has been oversimplified and values for the missing dimensions should be plugged in. A line is just a plane with a width of zero.

Kind of true. But not entirely, I think.
Though you can embed a finite dimensional space into a infinite dimensional space the two constructs have different proprieties and I don't think it's always possible to make a rigorous mapping between the two (of course from the latter to the former).
Also a dimension is not a place. This is the most common misconception upon which all the sci-fi movies and novel are written: go to the fifth dimension doesn't make sense to any mathematician and physicist. A dimension is a tool to make math works but it's not always the case, for instance in physics dimensions have a very "physical" meaning, and talking about a three dimensional space or a four dimensional one leads to very different solutions hence a very different physics. Also the signature of the metric is important: you can't have motion in 4D Euclidean space, to have motion you need the sign to be different in the time direction.

Infidel wrote:Most people think in terms of two opposing perspectives--linear two dimensional thinking.

Two dimensions can't be linear. I prefer them polar, but any other embedding works just fine.
In two dimensions one can not define greater and less, as for instance complex numbers can not be ordered.

Infidel wrote:I think three dimensionally, so sometimes I'm able to define lines, spheres and parabolas of arguments that do not intersect, at any point, with the common defined lines of existing argument.

Lines and parabolas can be defined in two dimensions, spheres can't (though a sphere in two dimension would be an S^1, but usually we call them circles).

Well if you assume the Axiom of Choice (which a very significant portion of Math depends on) any set can not only be ordered but it can be Well Ordered (may not be useful but it can be done)...

two_heads_talking wrote:What's that got to do with voting? I've made up my mind by the time I hit the booth. I'm not swayed by the knuckle draggers who stand outside holding up signs of their favorite candidate. I usually tell them to quit wasting their breath on me..

You know. Seeing both sides, yada yada yada. Staring at the ballot. Well, the R guy is good, but the D guy is good too...

Didn't say one can't define a line in two dimensions (of course it's possible), just said that in two dimensions the concept of linearly consecutive events, which is the base of linear thinking, is meaningless.
But then I prefer stringy over loopy ...

With what you've posted about your physics and other math abilities, I was playing devil's advocate with you.. I picked loopy especially because it is in almost complete opposition to stringy..

two_heads_talking wrote:
With what you've posted about your physics and other math abilities, I was playing devil's advocate with you.. I picked loopy especially because it is in almost complete opposition to stringy..

Sorry, I was just trying to be ultra-funny/antagonistic... /grin

No worries!
It's actually fun to be able to joke about Physics once in a while. People in my field are way too serious about it, and picky.
I do believe "The Big Bang Theory" is probably the best comedy on tv now. The stories are actually quite accurate, and so (some) of the Physics jokes ... though those guys have too much of a life to be physicists for real ...

two_heads_talking wrote:
Sorry, I knew what you meant, I was trying to play coy with you.. lol

I've always had trouble with "coy" -- as a cursory look at my pathetic dating history would show.

Lol, I thought you'd get a laugh out of it at least.. lol

two_heads_talking wrote:
With what you've posted about your physics and other math abilities, I was playing devil's advocate with you.. I picked loopy especially because it is in almost complete opposition to stringy..

Sorry, I was just trying to be ultra-funny/antagonistic... /grin

astaroth wrote:No worries!
It's actually fun to be able to joke about Physics once in a while. People in my field are way too serious about it, and picky.
I do believe "The Big Bang Theory" is probably the best comedy on tv now. The stories are actually quite accurate, and so (some) of the Physics jokes ... though those guys have too much of a life to be physicists for real ...

I'll admit, my physics is a bit rusty and my quantum theory is completely shot, but as an Engineer/Designer, I can 'fake' it sometimes. lol.

astaroth wrote:I do believe "The Big Bang Theory" is probably the best comedy on tv now. The stories are actually quite accurate, and so (some) of the Physics jokes ... though those guys have too much of a life to be physicists for real ...

astaroth wrote:I do believe "The Big Bang Theory" is probably the best comedy on tv now. The stories are actually quite accurate, and so (some) of the Physics jokes ... though those guys have too much of a life to be physicists for real ...

I *love* that show.

I find it amusing at times.. but mostly, I find myself wanting to punch Sheldon in the throat..